Exploring High-Order Structure for Robust Graph Structure Learning

Abstract: Recent studies show that Graph Neural Networks (GNNs) are vulnerable to adversarial attack, i.e., an imperceptible structure perturbation can fool GNNs to make wrong predictions. Some researches explore specific properties of clean graphs such as the feature smoothness to defense the attack, but the analysis of it has not been well-studied. In this paper, we analyze the adversarial attack on graphs from the perspective of feature smoothness which further contributes to an efficient new adversarial defensive algorithm for GNNs. We discover that the effect of the high-order graph structure is a smoother filter for processing graph structures. Intuitively, the high-order graph structure denotes the path number between nodes, where larger number indicates closer connection, so it naturally contributes to defense the adversarial perturbation. Further, we propose a novel algorithm that incorporates the high-order structural information into the graph structure learning. We perform experiments on three popular benchmark datasets, Cora, Citeseer and Polblogs. Extensive experiments demonstrate the effectiveness of our method for defending against graph adversarial attacks.